What is the value of b in the equation (y Superscript negative 9 Baseline) Superscript b Baseline = y Superscript 45?

Question

–405
–5
5
405

Answer 1

To solve the equation \( (y^{-9})^b = y^{45} \), we can use the property of exponents which states that \( (a^m)^n = a^{m \cdot n} \).

Applying this to our equation, we have:

\[ (y^{-9})^b = y^{-9b} \]

Now we can rewrite the equation:

\[ y^{-9b} = y^{45} \]

Since the bases (y) are the same, we can set the exponents equal to each other:

\[ -9b = 45 \]

Next, we solve for \( b \):

1. Divide both sides by -9:

\[ b = \frac{45}{-9} = -5 \]

Thus, the value of \( b \) is \( -5 \).

So the answer is:

–5