Solve ((3^9)^4x)^5y: Multi-Variable Nested Exponent Problem

Question

((39)4x)5y= ((3^9)^{4x)^{5y}}=

Video Solution

Solution Steps

00:00 Simplify the expression
00:03 When there is a power of a power, the combined exponent is the product of the exponents
00:10 Let's use this formula in our exercise
00:14 We'll multiply each of the exponents
00:21 We'll solve one multiplication at a time
00:33 And this is the solution to the question

Step-by-Step Solution

We use the power rule for an exponent raised to another exponent:

(am)n=amn (a^m)^n=a^{m\cdot n} We apply this rule to the given problem:

((39)4x)5y=(39)4x5y=394x5y=3180xy ((3^9)^{4x})^{5y}= (3^9)^{4x\cdot 5y} =3^{9\cdot4x\cdot 5y}=3^{180xy} In the first step we applied the previously mentioned power rule and removed the outer parentheses. In the next step we applied the power rule once again and removed the remaining parentheses. In the final step we simplified the resulting expression.

Therefore, the correct answer is option b.

Answer

3180xy 3^{180xy}