Question

simplify. express your answer using positive exponents. $5pqr^{4} cdot 2p^{9}q^{8}r^{62}$

Explanation:

Step1: Multiply the coefficients

Multiply 5 and 2.
$5\times2 = 10$

Step2: Multiply the powers of \( p \)

Use the rule \( a^m \cdot a^n = a^{m + n} \). For \( p \), we have \( p^1 \cdot p^9 = p^{1 + 9} = p^{10} \)

Step3: Multiply the powers of \( q \)

Using the same exponent rule, for \( q \), \( q^1 \cdot q^8 = q^{1 + 8} = q^9 \)

Step4: Multiply the powers of \( r \)

For \( r \), \( r^4 \cdot r^{62} = r^{4 + 62} = r^{66} \)

Step5: Combine all the terms

Multiply the coefficient with the variables: \( 10 \times p^{10} \times q^9 \times r^{66} \)

Answer:

\( 10p^{10}q^9r^{66} \)