By the Quotient Rule of Exponents, we know that (a/b)^n = a^n / b^n.
Therefore, we can rewrite the expression (5/6)^10 ÷ (⅖)^3 as:
(5^10 / 6^10) / (2^3 / 5^3)
= 5^10 / 6^10 * 5^3 / 2^3
= 5^13 / 6^10 * 2^3
= 5^13 * 2^3 / 6^10
= 5^13 * 8 / 6^10
= 5^13 * 8 / 2^10 * 3^10
= 5^13 * 4 * 2^4 / 2^10 * 3^10
= 5^13 * 4 / 3^10
Therefore, the final equivalent form with a whole number for the exponent is 5^13 * 4 / 3^10, which has an exponent of 13.
Applying the Quotient Rule of Exponents, what is the exponent in an equivalent form of
(5/6)^10 ÷ (⅖)^3? Answer with a whole number for the exponent.
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1 answer