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

Step-by-Step Solution

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

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

((39)4x)5y=(39)4x⋅5y=39⋅4x⋅5y=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}

More Questions

Related Subjects

Exponents and Exponent rules Rules of Exponentiation Combining Powers and Roots Properties of Exponents Power of a Power

Question Types

Applying Combined Exponents Rules: Variables in the exponent of the power Power of a Power: Variables in the exponent of the power