Question

multiplying powers
score: 1/3 penalty: none
question
fully simplify.
-15x²(x⁵y⁴)

Explanation:

Step1: Apply the distributive property

Multiply -15 with the terms inside the parentheses. Also, use the exponent rule \(a^m \cdot a^n = a^{m + n}\) for the \(x\) terms.
\(-15x^{2}(x^{5}y^{4})=-15\times(x^{2}\cdot x^{5})\times y^{4}\)

Step2: Simplify the \(x\) exponents

Using the rule \(a^m \cdot a^n = a^{m + n}\), for \(x^{2}\cdot x^{5}\), we add the exponents: \(2 + 5 = 7\).
So we have \(-15\times x^{7}\times y^{4}\)

Step3: Write the final simplified form

Multiply the coefficients (here the coefficient of \(x^7\) is -15 and for \(y^4\) is 1, so we just combine them).
\(-15x^{7}y^{4}\)

Answer:

\(-15x^{7}y^{4}\)