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What is the value of A when we rewrite ((1)/(8))^(x)+((1)/(8))^(x-2) as A*((1)/(8))^(x) ? A=

What is the value of A A when we rewrite (18)x+(18)x−2 \left(\frac{1}{8}\right)^{x}+\left(\frac{1}{8}\right)^{x-2} as A⋅(18)x A \cdot\left(\frac{1}{8}\right)^{x} ?\newlineA= A=

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Q. What is the value of A A when we rewrite (18)x+(18)x−2 \left(\frac{1}{8}\right)^{x}+\left(\frac{1}{8}\right)^{x-2} as A⋅(18)x A \cdot\left(\frac{1}{8}\right)^{x} ?\newlineA= A=
  1. Express with Same Exponent: First, we need to express both terms with the same base and exponent. The first term is already in the form we want, (18)x\left(\frac{1}{8}\right)^x. We need to manipulate the second term, (18)x−2\left(\frac{1}{8}\right)^{x-2}, to have the same exponent as the first term.
  2. Apply Exponent Property: To do this, we can use the property of exponents that states a(m−n)=amana^{(m-n)} = \frac{a^m}{a^n}. We apply this to the second term to get (18)x/(18)2\left(\frac{1}{8}\right)^x / \left(\frac{1}{8}\right)^2.
  3. Rewrite Second Term: Since (18)2\left(\frac{1}{8}\right)^2 is equal to 164\frac{1}{64}, we can rewrite the second term as (18)x⋅(1164)\left(\frac{1}{8}\right)^x \cdot \left(\frac{1}{\frac{1}{64}}\right) or (18)x⋅64\left(\frac{1}{8}\right)^x \cdot 64.
  4. Factor Out Common Term: Now we have the expression ((1)/(8))x+64∗((1)/(8))x((1)/(8))^x + 64*((1)/(8))^x. We can factor out ((1)/(8))x((1)/(8))^x to get ((1)/(8))x∗(1+64)((1)/(8))^x * (1 + 64).
  5. Calculate Final Value: Adding 1+641 + 64 gives us 6565. So the expression becomes 65×(18)x65 \times \left(\frac{1}{8}\right)^x.
  6. Calculate Final Value: Adding 1+641 + 64 gives us 6565. So the expression becomes 65×(18)x65 \times \left(\frac{1}{8}\right)^x.Therefore, the value of AA when we rewrite (18)x+(18)x−2\left(\frac{1}{8}\right)^x + \left(\frac{1}{8}\right)^{x-2} as A×(18)xA\times\left(\frac{1}{8}\right)^x is 6565.

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