Simplify the following expressions: a) (−21a5b4)/(−3a4b) b) (2x4y7)3

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ScanSolve AI Tutor · Accepted Answer

a) Step 1: Divide the numerical coefficients. (−21)/(−3) = 7; Step 2: Divide the terms with base a using the exponent rule (x^m)/(xⁿ) = x^(m−n). (a⁵)/(a⁴) = a⁵⁻⁴ = a¹ = a; Step 3: Divide the terms with base b using the exponent rule (x^m)/(xⁿ) = x^(m−n) (note that b = b¹). (b⁴)/(b¹) = b⁴⁻¹ = b³ Step 4: Combine the results. 7ab³ The final answer is 7ab³. b) Step 1: Apply the exponent 3 to each factor inside the parentheses using the rule (xyz)ⁿ = xⁿ yⁿ zⁿ. (2 x⁴ y⁷)³ = 2³ (x⁴)³ (y⁷)³ Step 2: Calculate 2³. 2³ = 2 × 2 × 2 = 8; Step 3: Apply the exponent 3 to the variable terms using the rule (x^m)ⁿ = x^(mn). (x⁴)³ = x^(4 × 3) = x¹²; (y⁷)³ = y^(7 × 3) = y²¹ Step 4: Combine the results. 8x¹²y²¹ The final answer is 8x¹²y²¹.

Simplify the following expressions: a) (-21a5b4)/(-3a4b) b) (2x4y7)3

Answers

Step-by-step solution

Part a· 4 steps

Divide the numerical coefficients.

Divide the terms with base $a$ using the exponent rule $\frac{x^m}{x^n} = x^{m-n}$ .

Divide the terms with base $b$ using the exponent rule $\frac{x^m}{x^n} = x^{m-n}$ (note that $b = b^1$ ).

Combine the results.

Part b· 4 steps
$8x^{12}y^{21}$

Apply the exponent 3 to each factor inside the parentheses using the rule $(xyz)^n = x^n y^n z^n$ .

Calculate $2^3$ .

Apply the exponent 3 to the variable terms using the rule $(x^m)^n = x^{mn}$ .

Combine the results.

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Simplify the following expressions: a) (-21a5b4)/(-3a4b) b) (2x4y7)3

Answers

Step-by-step solution

Part a· 4 steps

Divide the numerical coefficients.

Divide the terms with base aaa using the exponent rule xmxn=xm−n\frac{x^m}{x^n} = x^{m-n}xnxm​=xm−n.

Divide the terms with base bbb using the exponent rule xmxn=xm−n\frac{x^m}{x^n} = x^{m-n}xnxm​=xm−n (note that b=b1b = b^1b=b1).

Combine the results.

Part b· 4 steps8x12y218x^{12}y^{21}8x12y21

Apply the exponent 3 to each factor inside the parentheses using the rule (xyz)n=xnynzn(xyz)^n = x^n y^n z^n(xyz)n=xnynzn.

Calculate 232^323.

Apply the exponent 3 to the variable terms using the rule (xm)n=xmn(x^m)^n = x^{mn}(xm)n=xmn.

Combine the results.

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More Mathematics Questions

Divide the terms with base $a$ using the exponent rule $\frac{x^m}{x^n} = x^{m-n}$ .

Divide the terms with base $b$ using the exponent rule $\frac{x^m}{x^n} = x^{m-n}$ (note that $b = b^1$ ).

Part b· 4 steps
$8x^{12}y^{21}$

Apply the exponent 3 to each factor inside the parentheses using the rule $(xyz)^n = x^n y^n z^n$ .

Calculate $2^3$ .

Apply the exponent 3 to the variable terms using the rule $(x^m)^n = x^{mn}$ .