Video Transcript
Given that four-fifths to the power of 𝑥 plus seven is equal to 64 over 125, determine the value of 𝑥.
We can begin this question by recognizing that four cubed is equal to 64 and five cubed is equal to 125. One of our laws of exponents states that 𝑎 to the power of 𝑥 divided by 𝑏 to the power of 𝑥 is equal to 𝑎 over 𝑏 all raised to the power of 𝑥. This means we can rewrite the right-hand side of our equation as four-fifths cubed. This is equal to four-fifths to the power of 𝑥 plus seven.
The base of both sides of our equation is four-fifths. This means that the exponents must be equal. 𝑥 plus seven is equal to three. Subtracting seven from both sides of this equation gives us 𝑥 is equal to negative four.
This means that the value of 𝑥 that satisfies the equation four-fifths to the power of 𝑥 plus seven is equal to 64 over 125 is negative four.
