Question

Indicate whether each expression is equivalent or not equivalent to 7^8x7^-7

Answer 1

The expressions are equivalent.

Step-by-step explanation:

The given expression is
`\(7^8 * 7^(-7)\).` Using the properties of exponents, we can simplify this expression:

`\[ 7^8 * 7^(-7) = 7^(8 - 7) = 7^1 = 7 \]`

Now, let's evaluate each expression and compare:

1.
`\(7^1\):` This is equivalent to the original expression, as shown above.

2.
`\(7^(15) / 7^7\):` Using the quotient rule of exponents
`(\(a^m / a^n = a^(m-n)\)), we get \(7^(15-7) = 7^8\),` which is equivalent to the original expression.

3.
`\(7^5 * 7^3\):` Using the product rule of exponents
`(\(a^m * a^n = a^(m+n)\)),` we get
`\(7^(5+3) = 7^8\),` which is equivalent to the original expression.

4.
`\(7^9 / 7^2\)`: Using the quotient rule, we get
`\(7^(9-2) = 7^7\),` which is not equivalent to the original expression.

Therefore, three out of the four expressions are equivalent to
`\(7^8 * 7^(-7)\).`