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Simplify. Express your answer using positive exponents.\newline(4z4)(4z4)(10z2)(4z^4)(4z^4)(10z^2)

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Simplify exponential expressions using the multiplication and division rulesright chevron icon

Full solution

Q. Simplify. Express your answer using positive exponents.\newline(4z4)(4z4)(10z2)(4z^4)(4z^4)(10z^2)
  1. Group coefficients and powers: Group the coefficients and the powers of zz.(4z4)(4z4)(10z2)=(4×4×10)×(z4×z4×z2)(4z^4)(4z^4)(10z^2) = (4 \times 4 \times 10) \times (z^4 \times z^4 \times z^2)
  2. Calculate coefficient product: Calculate the product of the coefficients. 4×4×10=1604 \times 4 \times 10 = 160
  3. Combine powers using rule of exponents: Use the rule of exponents to combine the powers of zz.z4×z4×z2=z(4+4+2)=z10z^4 \times z^4 \times z^2 = z^{(4+4+2)} = z^{10}
  4. Write simplified expression: Combine the results from steps 22 and 33 to write the simplified expression.\newline160×z10=160z10160 \times z^{10} = 160z^{10}

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