If a number is raised to the second power, like 52{\displaystyle 5^{2}}, you can also say that the number is squared, such as “five squared. " If a number is raised to the third power, like 103{\displaystyle 10^{3}}, you can also say it is cubed, such as “ten cubed. " If a number has no exponent shown, like a simple 4, it is technically to the first power and can be rewritten as 41{\displaystyle 4^{1}}. If the exponent is 0, and a “non-zero number” is raised to the “zero power”, then the whole thing equals 1, such as 40=1{\displaystyle 4^{0}=1} or even something like (3/8)0=1. {\displaystyle (3/8)^{0}=1. } There is more about this in the “Tips” section.
If a number is raised to the second power, like 52{\displaystyle 5^{2}}, you can also say that the number is squared, such as “five squared. " If a number is raised to the third power, like 103{\displaystyle 10^{3}}, you can also say it is cubed, such as “ten cubed. " If a number has no exponent shown, like a simple 4, it is technically to the first power and can be rewritten as 41{\displaystyle 4^{1}}. If the exponent is 0, and a “non-zero number” is raised to the “zero power”, then the whole thing equals 1, such as 40=1{\displaystyle 4^{0}=1} or even something like (3/8)0=1. {\displaystyle (3/8)^{0}=1. } There is more about this in the “Tips” section.
If a number is raised to the second power, like 52{\displaystyle 5^{2}}, you can also say that the number is squared, such as “five squared. " If a number is raised to the third power, like 103{\displaystyle 10^{3}}, you can also say it is cubed, such as “ten cubed. " If a number has no exponent shown, like a simple 4, it is technically to the first power and can be rewritten as 41{\displaystyle 4^{1}}. If the exponent is 0, and a “non-zero number” is raised to the “zero power”, then the whole thing equals 1, such as 40=1{\displaystyle 4^{0}=1} or even something like (3/8)0=1. {\displaystyle (3/8)^{0}=1. } There is more about this in the “Tips” section.
If a number is raised to the second power, like 52{\displaystyle 5^{2}}, you can also say that the number is squared, such as “five squared. " If a number is raised to the third power, like 103{\displaystyle 10^{3}}, you can also say it is cubed, such as “ten cubed. " If a number has no exponent shown, like a simple 4, it is technically to the first power and can be rewritten as 41{\displaystyle 4^{1}}. If the exponent is 0, and a “non-zero number” is raised to the “zero power”, then the whole thing equals 1, such as 40=1{\displaystyle 4^{0}=1} or even something like (3/8)0=1. {\displaystyle (3/8)^{0}=1. } There is more about this in the “Tips” section.
45=4∗4∗4∗4∗4{\displaystyle 4^{5}=44444} 82=8∗8{\displaystyle 8^{2}=88} Ten cubed =10∗10∗10{\displaystyle =1010*10}[1] X Research source
45=4∗4∗4∗4∗4{\displaystyle 4^{5}=44444} 4∗4=16{\displaystyle 44=16} 45=16∗4∗4∗4{\displaystyle 4^{5}=16444}
45=16∗4∗4∗4{\displaystyle 4^{5}=16444} 16∗4=64{\displaystyle 164=64} 45=64∗4∗4{\displaystyle 4^{5}=6444} 64∗4=256{\displaystyle 644=256} 45=256∗4{\displaystyle 4^{5}=2564} 256∗4=1024{\displaystyle 2564=1024} As shown, you continue multiplying the base by your product of each first pair of numbers until you get your final answer. Simply keep multiplying the first two numbers, then multiply the answer by the next number in the sequence. This works for any exponent. Once you’re done with our example, you should get 45=4∗4∗4∗4∗4=1024{\displaystyle 4^{5}=4444*4=1024}.
64∗4=256{\displaystyle 64*4=256}
256∗4=1024{\displaystyle 256*4=1024}
82{\displaystyle 8^{2}} 34{\displaystyle 3^{4}} 107{\displaystyle 10^{7}}
Google the expression to check your answer. You can use the “^” button on your computer, tablet or smart phone keyboard to input an expression into Google search, which will spit out an instant answer, and suggest similar expressions to explore.
32+32=2∗32{\displaystyle 3^{2}+3^{2}=23^{2}} 45+45+45=3∗45{\displaystyle 4^{5}+4^{5}+4^{5}=34^{5}} 45−45+2=2{\displaystyle 4^{5}-4^{5}+2=2} 4x2−2x2=2x2{\displaystyle 4x^{2}-2x^{2}=2x^{2}}
x2∗x5{\displaystyle x^{2}x^{5}} x2=x∗x{\displaystyle x^{2}=xx} x5=x∗x∗x∗x∗x{\displaystyle x^{5}=xxxxx} x2∗x5=(x∗x)∗(x∗x∗x∗x∗x){\displaystyle x^{2}x^{5}=(xx)(xxxxx)} Since everything is just the same number multiplied, we can combine them: x2∗x5=x∗x∗x∗x∗x∗x∗x{\displaystyle x^{2}x^{5}=xxxxxxx} x2∗x5=x7{\displaystyle x^{2}*x^{5}=x^{7}}[4] X Research source
(x2)5{\displaystyle (x^{2})^{5}} (x2)5=x2∗x2∗x2∗x2∗x2{\displaystyle (x^{2})^{5}=x^{2}*x^{2}*x^{2}*x^{2}*x^{2}} Since the base bases are the same, you can simply add them together: (x2)5=x2∗x2∗x2∗x2∗x2=x10{\displaystyle (x^{2})^{5}=x^{2}*x^{2}*x^{2}*x^{2}*x^{2}=x^{10}}
5−101510{\displaystyle 5^{-10}{\frac {1}{5^{10}}}} 3x−4=3x4{\displaystyle 3x^{-}4={\frac {3}{x^{4}}}}[7] X Research source
As you’ll soon see, any number that is part of a fraction, like 142{\displaystyle {\frac {1}{4^{2}}}}, can actually be rewritten as 4−2{\displaystyle 4^{-2}}. Negative exponents create fractions.
As you’ll soon see, any number that is part of a fraction, like 142{\displaystyle {\frac {1}{4^{2}}}}, can actually be rewritten as 4−2{\displaystyle 4^{-2}}. Negative exponents create fractions.
53{\displaystyle 5^{3}} = 125 22+22+22{\displaystyle 2^{2}+2^{2}+2^{2}} = 12 x12−2x12{\displaystyle x^{1}2-2x^{1}2} = -x^12 y3∗y{\displaystyle y^{3}*y} = y4{\displaystyle y^{4}} Remember, a number without a power has an exponent of 1 (Q3)5{\displaystyle (Q^{3})^{5}} = Q15{\displaystyle Q^{1}5} r5r2{\displaystyle {\frac {r^{5}}{r^{2}}}} = r3{\displaystyle r^{3}}[8] X Research source
Roots are the inverse of exponents. For example, if you took the answer to x4{\displaystyle {\sqrt[{4}]{x}}} raised it to the fourth power, you would be back at x{\displaystyle x}, such as 164=2{\displaystyle {\sqrt[{4}]{16}}=2} can be checked as 24=16{\displaystyle 2^{4}=16}. Also for example, if x4=2{\displaystyle {\sqrt[{4}]{x}}=2} then 24=x{\displaystyle 2^{4}=x} therefore x=2{\displaystyle x=2} .
x53{\displaystyle x^{\frac {5}{3}}} x53=(x5)13{\displaystyle x^{\frac {5}{3}}=(x^{5})^{\frac {1}{3}}} or x53=(x13)5{\displaystyle x^{\frac {5}{3}}=(x^{\frac {1}{3}})^{5}} x13=x3{\displaystyle x^{\frac {1}{3}}={\sqrt[{3}]{x}}} x53{\displaystyle x^{\frac {5}{3}}} = (x3)5{\displaystyle ({\sqrt[{3}]{x}})^{5}}
x53+x53=2(x53){\displaystyle x^{\frac {5}{3}}+x^{\frac {5}{3}}=2(x^{\frac {5}{3}})} x53∗x23=x73{\displaystyle x^{\frac {5}{3}}*x^{\frac {2}{3}}=x^{\frac {7}{3}}}[10] X Research source
