Question

simplify. give answers using positive exponents.
$(7x^{4}y^{7})^{2}$

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So, for \((7x^{4}y^{7})^{2}\), we can apply this rule to each factor inside the parentheses: \(7^{2}(x^{4})^{2}(y^{7})^{2}\).

Step2: Simplify each term

• For the constant term: \(7^{2}=49\).
• For the \(x\)-term, use the power of a power rule \((a^{m})^{n}=a^{mn}\): \((x^{4})^{2}=x^{4\times2}=x^{8}\).
• For the \(y\)-term, also use the power of a power rule: \((y^{7})^{2}=y^{7\times2}=y^{14}\).

Step3: Combine the simplified terms

Multiply the simplified terms together: \(49\times x^{8}\times y^{14}=49x^{8}y^{14}\).

Answer:

\(49x^{8}y^{14}\)