Question

which expression is equivalent to 40x^-3y^5/8x^-2y^-2

Answer 1

the expression (x^13)(x^4)^2 is equivalent to x^p. what is the value of p?

Answer 2

To simplify the expression \(\frac{40x^{-3}y^5}{8x^{-2}y^{-2}}\), follow these steps:

1. **Simplify the coefficients:**
\[
\frac{40}{8} = 5
\]

2. **Use the properties of exponents to simplify the variables \(x\):**
\[
\frac{x^{-3}}{x^{-2}} = x^{-3 - (-2)} = x^{-3 + 2} = x^{-1}
\]

3. **Use the properties of exponents to simplify the variables \(y\):**
\[
\frac{y^5}{y^{-2}} = y^{5 - (-2)} = y^{5 + 2} = y^7
\]

Putting it all together:

\[
\frac{40x^{-3}y^5}{8x^{-2}y^{-2}} = 5x^{-1}y^7
\]

Since \(x^{-1} = \frac{1}{x}\), the expression can also be written as:

\[
5x^{-1}y^7 = \frac{5y^7}{x}
\]

Thus, the simplified expression equivalent to \(\frac{40x^{-3}y^5}{8x^{-2}y^{-2}}\) is \(\boxed{\frac{5y^7}{x}}\).

Answer 3

To simplify the expression \((x^{13})(x^4)^2\) and express it in the form \(x^p\), follow these steps:

1. Start with the expression:
\[
(x^{13})(x^4)^2
\]

2. Apply the power rule for exponents to \( (x^4)^2 \):
\[
(x^4)^2 = x^{4 \cdot 2} = x^8
\]

3. Now the expression becomes:
\[
x^{13} \cdot x^8
\]

4. Use the product rule for exponents to combine the exponents:
\[
x^{13 + 8} = x^{21}
\]

Therefore, the expression \((x^{13})(x^4)^2\) is equivalent to \(x^{21}\), and the value of \(p\) is \(\boxed{21}\).