- When multiplying terms with the same base, add the exponents: $p^5 \cdot p^2 = p^{5+2} = p^7$, $m^3 \cdot m^2 = m^{3+2} = m^5$.
- Multiply the coefficients: $10 \cdot 4 = 40$.
- Combine to get $40p^7m^5$.
- When multiplying terms with the same base, add the exponents: $t^3 \cdot t = t^{3+1} = t^4$, $w^3 \cdot w^4 = w^{3+4} = w^7$.
- Multiply the coefficients: $10 \cdot 2 = 20$.
- Combine to get $20t^4w^7$.
- When multiplying terms with the same base, add the exponents: $p^6 \cdot p^3 = p^{6+3} = p^9$, $t^2 \cdot t = t^{2+1} = t^3$.
- Multiply the coefficients: $2 \cdot 5 = 10$.
- Combine to get $10p^9t^3$.
- When multiplying terms with the same base, add the exponents: $y \cdot y^6 = y^{1+6} = y^7$, $w^4 \cdot w^3 = w^{4+3} = w^7$.
- Multiply the coefficients: $2 \cdot 2 = 4$.
- Combine to get $4y^7w^7$.
- When multiplying terms with the same base, add the exponents: $a^5 \cdot a^5 = a^{5+5} = a^{10}$, $g^4 \cdot g = g^{4+1} = g^5$.
- Multiply the coefficients: $10 \cdot 4 = 40$.
- Combine to get $40a^{10}g^5$.
- When multiplying terms with the same base, add the exponents: $f^3 \cdot f^5 = f^{3+5} = f^8$, $v \cdot v^2 = v^{1+2} = v^3$.
- Multiply the coefficients: $4 \cdot 2 = 8$.
- Combine to get $8f^8v^3$.
- Cancel common factors in numerator and denominator. The $w^2$ cancels out. Divide coefficients: $20/50 = 2/5$. Subtract exponents for $n$: $n^1 / n^4 = n^{1-4} = n^{-3} = 1/n^3$.
- Result is $2/(5n^3)$.
- Cancel common factors. The $p^3$ cancels with part of $p^5$, leaving $p^{5-3} = p^2$ in the denominator. Divide coefficients: $5/50 = 1/10$. Subtract exponents for $v$: $v^4 / v^5 = v^{4-5} = v^{-1} = 1/v$.
- Result is $1/(10p^2v)$.
- Cancel common factors. The $u^5$ cancels with part of $u^6$, leaving $u^{6-5} = u$ in the numerator. The $f^3$ cancels with part of $f^5$, leaving $f^{5-3} = f^2$ in the denominator. Divide coefficients: $3/30 = 1/10$.
- Result is $uf^2/10$.
- Cancel common factors. The $v^3$ cancels with part of $v^6$, leaving $v^{6-3} = v^3$ in the denominator. The $t^4$ cancels with part of $t^6$, leaving $t^{6-4} = t^2$ in the denominator. Divide coefficients: $20/8 = 5/2$.
- Result is $5v^2/(2t^2)$.
- Cancel common factors. The $f^4$ cancels with part of $f^2$, leaving $f^{4-2} = f^2$ in the numerator. The $q$ cancels with part of $q^5$, leaving $q^{5-1} = q^4$ in the denominator. Divide coefficients: $8/12 = 2/3$.
- Result is $2f^2/(3q^4)$.
- Cancel common factors. The $g^5$ cancels with part of $g^5$, leaving 1. The $r^5$ cancels with part of $r^5$, leaving 1. The $q^3$ cancels with part of $q^3$, leaving 1. Divide coefficients: $10/20 = 1/2$.
- Result is $1/(2g^2)$.
Parent Tip: Review the logic above to help your child master the concept of exponents and multiplication worksheet.
