how can i use the law of exponents to simplify:
(6 ^5/8)^2/9
5/8 fraction
2/9 fraction
(xa)b = (x)ab
follow that rule, let me know what you get.
would it be (6)^61/72?
To simplify the expression (6^(5/8))^(2/9) using the law of exponents, we need to understand a few rules:
Rule 1: When raising a power to another power, multiply the exponents.
Rule 2: When there is a fractional exponent, it represents taking the root of the base.
Let's apply these rules step by step:
Step 1: Begin by applying Rule 2 to the numerator exponent, (5/8). Since the exponent is 5/8, it means taking the 8th root of 6 raised to the power of 5: ∛(6^5).
Step 2: Now, using Rule 1, we multiply the exponents 5/8 and 2/9: ∛(6^((5/8) * (2/9))).
Step 3: Simplify the exponent by calculating (5/8) * (2/9), which evaluates to 10/72 or 5/36: ∛(6^(5/36)).
Therefore, the simplified form of (6^(5/8))^(2/9) is ∛(6^(5/36)).