Fully simplify. 10x^(3)y^(2)(8x^(4)y^(5)) Answer:

Multiply Coefficients and Apply Product Rule: To simplify the expression, we need to multiply the coefficients (numerical values) together and apply the product rule for exponents, which states that when multiplying like bases, we add the exponents. Calculation: 10 * 8 = 80 Math error check: 10 * 8 is indeed 80. Apply Product Rule to x Terms: Now we apply the product rule to the x terms. The product rule for exponents states that x^(a) * x^(b) = x^(a+b). Calculation: x^(3) * x^(4) = x^(3+4) = x^(7) Math error check: Adding the exponents 3 and 4 correctly gives us 7. Apply Product Rule to y Terms: Next, we apply the product rule to the y terms in the same way. Calculation: y^(2) * y^(5) = y^(2+5) = y^(7) Math error check: Adding the exponents 2 and 5 correctly gives us 7. Combine Results for Fully Simplified Expression: Finally, we combine the results from the previous steps to write the fully simplified expression. Calculation: 80x^(7)y^(7) Math error check: The coefficients and exponents have been correctly combined.

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Q. Fully simplify.

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10 x^{3} y^{2}\left(8 x^{4} y^{5}\right)

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Answer:

Multiply Coefficients and Apply Product Rule: To simplify the expression, we need to multiply the coefficients (numerical values) together and apply the product rule for exponents, which states that when multiplying like bases, we add the exponents. $\newline$ Calculation: $10 \times 8 = 80$ $\newline$ Math error check: $10 \times 8$ is indeed $80$ .
Apply Product Rule to x Terms: Now we apply the product rule to the x terms. The product rule for exponents states that $x^{a} \times x^{b} = x^{a+b}$ . $\newline$ Calculation: $x^{3} \times x^{4} = x^{3+4} = x^{7}$ $\newline$ Math error check: Adding the exponents $3$ and $4$ correctly gives us $7$ .
Apply Product Rule to $y$ Terms: Next, we apply the product rule to the $y$ terms in the same way. $\newline$ Calculation: $y^{2} \times y^{5} = y^{2+5} = y^{7}$ $\newline$ Math error check: Adding the exponents $2$ and $5$ correctly gives us $7$ .
Combine Results for Fully Simplified Expression: Finally, we combine the results from the previous steps to write the fully simplified expression. $\newline$ Calculation: $80x^{7}y^{7}$ $\newline$ Math error check: The coefficients and exponents have been correctly combined.