Simplify the following algebraic expressions: 1) (6a2 b2)/(3a5 b3) 2) (45×3 b7)/(3×4 b2) 3) (21t3 y + 7t2 y2…

Question

Simplify the following algebraic expressions: 1) (6a2 b2)/(3a5 b3) 2) (45×3 b7)/(3×4 b2) 3) (21t3 y + 7t2 y2 + 28ty7)/(14t5 y3)

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for simplifying the algebraic expressions:

1) Simplify $\frac{6a^2 b^2}{3a^5 b^3}$

Simplify the coefficients and apply the exponent rule $\frac{x^m}{x^n} = x^{m-n}$ to the variables.
$\frac{6a^2 b^2}{3a^5 b^3} = \frac{6}{3} \cdot a^{2-5} \cdot b^{2-3}$
Perform the subtractions in the exponents and simplify the fraction.
$2 \cdot a^{-3} \cdot b^{-1}$
Rewrite terms with negative exponents using $x^{-n} = \frac{1}{x^n}$ .
$\frac{2}{a^3 b^1}$ $\boxed{\frac{2}{a^3 b}}$
2) Simplify $\frac{45x^3 b^7}{3x^4 b^2}$
Simplify the coefficients and apply the exponent rule $\frac{x^m}{x^n} = x^{m-n}$ to the variables.
$\frac{45x^3 b^7}{3x^4 b^2} = \frac{45}{3} \cdot x^{3-4} \cdot b^{7-2}$
Perform the subtractions in the exponents and simplify the fraction.
$15 \cdot x^{-1} \cdot b^5$
Rewrite terms with negative exponents using $x^{-n} = \frac{1}{x^n}$ .
$\frac{15b^5}{x^1}$ $\boxed{\frac{15b^5}{x}}$
3) Simplify $\frac{21t^3 y + 7t^2 y^2 + 28ty^7}{14t^5 y^3}$
Divide each term in the numerator by the denominator.
$\frac{21t^3 y}{14t^5 y^3} + \frac{7t^2 y^2}{14t^5 y^3} + \frac{28ty^7}{14t^5 y^3}$
Simplify each fraction by dividing coefficients and applying the exponent rule $\frac{x^m}{x^n} = x^{m-n}$ .
$\frac{3}{2} t^{3-5} y^{1-3} + \frac{1}{2} t^{2-5} y^{2-3} + \frac{2}{1} t^{1-5} y^{7-3}$ $\frac{3}{2} t^{-2} y^{-2} + \frac{1}{2} t^{-3} y^{-1} + 2 t^{-4} y^4$
Rewrite terms with negative exponents using $x^{-n} = \frac{1}{x^n}$ .
$\frac{3}{2t^2 y^2} + \frac{1}{2t^3 y} + \frac{2y^4}{t^4}$ $\boxed{\frac{3}{2t^2 y^2} + \frac{1}{2t^3 y} + \frac{2y^4}{t^4}}$
4) Simplify $\frac{33p^0 z^3 - 11p^2 z^3}{22p^5 z^2}$
Simplify $p^0 = 1$ .
$\frac{33(1)z^3 - 11p^2 z^3}{22p^5 z^2} = \frac{33z^3 - 11p^2 z^3}{22p^5 z^2}$
Divide each term in the numerator by the denominator.
$\frac{33z^3}{22p^5 z^2} - \frac{11p^2 z^3}{22p^5 z^2}$
Simplify each fraction by dividing coefficients and applying the exponent rule $\frac{x^m}{x^n} = x^{m-n}$ .
$\frac{3}{2} p^{0-5} z^{3-2} - \frac{1}{2} p^{2-5} z^{3-2}$ $\frac{3}{2} p^{-5} z^1 - \frac{1}{2} p^{-3} z^1$
Rewrite terms with negative exponents using $x^{-n} = \frac{1}{x^n}$ .
$\frac{3z}{2p^5} - \frac{z}{2p^3}$ $\boxed{\frac{3z}{2p^5} - \frac{z}{2p^3}}$

Simplify the following algebraic expressions: 1) (6a2 b2)/(3a5 b3) 2) (45x3 b7)/(3x4 b2) 3) (21t3 y + 7t2 y2 + 28ty7)/(14t5 y3)

Step-by-step solution

Simplify the coefficients and apply the exponent rule $\frac{x^m}{x^n} = x^{m-n}$ to the variables.

Perform the subtractions in the exponents and simplify the fraction.

Rewrite terms with negative exponents using $x^{-n} = \frac{1}{x^n}$ .

Simplify the coefficients and apply the exponent rule $\frac{x^m}{x^n} = x^{m-n}$ to the variables.

Perform the subtractions in the exponents and simplify the fraction.

Rewrite terms with negative exponents using $x^{-n} = \frac{1}{x^n}$ .

Divide each term in the numerator by the denominator.

Simplify each fraction by dividing coefficients and applying the exponent rule $\frac{x^m}{x^n} = x^{m-n}$ .

Rewrite terms with negative exponents using $x^{-n} = \frac{1}{x^n}$ .

Simplify $p^0 = 1$ .

Divide each term in the numerator by the denominator.

Simplify each fraction by dividing coefficients and applying the exponent rule $\frac{x^m}{x^n} = x^{m-n}$ .

Rewrite terms with negative exponents using $x^{-n} = \frac{1}{x^n}$ .

Still stuck on this one?

More Mathematics Questions

Simplify the following algebraic expressions: 1) (6a2 b2)/(3a5 b3) 2) (45x3 b7)/(3x4 b2) 3) (21t3 y + 7t2 y2 + 28ty7)/(14t5 y3)

Step-by-step solution

Simplify the coefficients and apply the exponent rule xmxn=xm−n\frac{x^m}{x^n} = x^{m-n}xnxm​=xm−n to the variables.

Perform the subtractions in the exponents and simplify the fraction.

Rewrite terms with negative exponents using x−n=1xnx^{-n} = \frac{1}{x^n}x−n=xn1​.

Simplify the coefficients and apply the exponent rule xmxn=xm−n\frac{x^m}{x^n} = x^{m-n}xnxm​=xm−n to the variables.

Perform the subtractions in the exponents and simplify the fraction.

Rewrite terms with negative exponents using x−n=1xnx^{-n} = \frac{1}{x^n}x−n=xn1​.

Divide each term in the numerator by the denominator.

Simplify each fraction by dividing coefficients and applying the exponent rule xmxn=xm−n\frac{x^m}{x^n} = x^{m-n}xnxm​=xm−n.

Rewrite terms with negative exponents using x−n=1xnx^{-n} = \frac{1}{x^n}x−n=xn1​.

Simplify p0=1p^0 = 1p0=1.

Divide each term in the numerator by the denominator.

Simplify each fraction by dividing coefficients and applying the exponent rule xmxn=xm−n\frac{x^m}{x^n} = x^{m-n}xnxm​=xm−n.

Rewrite terms with negative exponents using x−n=1xnx^{-n} = \frac{1}{x^n}x−n=xn1​.

Still stuck on this one?

More Mathematics Questions

Simplify the coefficients and apply the exponent rule $\frac{x^m}{x^n} = x^{m-n}$ to the variables.

Rewrite terms with negative exponents using $x^{-n} = \frac{1}{x^n}$ .

Simplify the coefficients and apply the exponent rule $\frac{x^m}{x^n} = x^{m-n}$ to the variables.

Rewrite terms with negative exponents using $x^{-n} = \frac{1}{x^n}$ .

Simplify each fraction by dividing coefficients and applying the exponent rule $\frac{x^m}{x^n} = x^{m-n}$ .

Rewrite terms with negative exponents using $x^{-n} = \frac{1}{x^n}$ .

Simplify $p^0 = 1$ .

Simplify each fraction by dividing coefficients and applying the exponent rule $\frac{x^m}{x^n} = x^{m-n}$ .

Rewrite terms with negative exponents using $x^{-n} = \frac{1}{x^n}$ .