laws of exponents

When multiplying powers with the same base, you ADD exponents.

ex: $5^8\cdot5^3$ = $5^{11}$

When dividing powers with the same base, you SUBTRACT the exponents.

ex: $5^8\div5^3$ = $5^5$

To raise a power to a power, MULTIPLY the exponents.

ex: ${5^4}^2$ = $5^8$

When a product is raised to an exponent, you can rewrite each factor in the product with the same exponent.

ex: (3)(4) $^3$ = ( $3^3$ ) ( $4^3$ )

When a quotient is raised to an exponent, you can rewrite each number in the quotient with the same exponent.

ex: $\frac{1}{2}^3$ = $1^3$ ÷ $2^3$

When the exponent of a power is zero, the value of the power is 1 (as long as the base is not zero).

ex: $3^4$ ÷ $3^4$ = 1

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