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3 years ago

Use the quotient of powers property to simplify the numeric expression.

Mathematics

1 answer:

Alex17521 [72]3 years ago

3 0

Answer:

$2^{\frac{3}{10}}$

Step-by-step explanation:

$\frac{2^{\frac{2}{5}}}{2^{\frac{1}{10}}}$

Applying quotient of powers property (i.e. $\frac{a^x}{a^y} = a^{x - y}$

$2^{\frac{2}{5} - \frac{1}{10}}$

$2^{\frac{4 - 1}{10}}$

$2^{\frac{3}{10}}$

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Answer: " x = 12 " .

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Step-by-step explanation:

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Note: If 2 (two) triangles are "similar" ; then their corresponding sides are "proportional".

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Since one of the sides [the "hypotenuse"] of one the triangles given ; shows the measurement containing an expression with a value of "x" — specifically; " 6x + 28 " ;

→ And since we want to solve for the value of "x" ; we use this "hypotenuse" of said particular triangle to set up a "proportion" with corresponding sides; so we can solve for "x" :

→ Set up proportions as a "ratio" ; or fraction:

→ 7:28::25:(6x + 28) ; Solve for "x" ;

Let us write this in the form of a "fraction" :

→ $\frac{7}{28} = \frac{25}{(6x+28)}$ ;

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Note:

→ Rewrite: " $\frac{7}{28}$ " ; by simplifying to:

" $\frac{1}{4}$ " ;

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→ Since: " $\frac{7}{28}$ " ;

= " (7÷7) / (28÷7) " ;

= " (1 /4) " ;

= " $\frac{1}{4}$ " .

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Now, rewrite the "proportion" ; as follows:

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$\frac{1}{4} = \frac{25}{(6x+28)}$ ;

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Now: "Cross multiply" ; that is:

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→ Given: " $\frac{a}{b} = \frac{c}{d}$ " ;

and: " b $\neq$ 0 " ; " d $\neq$ 0 " ;

→ Then: " a * d " = " b * c " .

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Likewise: " 1(6x + 28) = (4) * (25) " ;

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SImplify: " 6x + 28 = 100 " ; Solve for "x" ;

→ Subtract "28" from each side of the equation:

→ " 6x + 28 - 28 = 100 - 28 " ;

to get: → " 6x = 72 " ;

Now, divide each side of the equation by: " 6 " ;

to isolate "x" on one side of the equation; & to solve for "x" ; as follows:

→ " 6x = 72 " ;

→ 6x / 6 = 72 / 6 ;

to get:

→ " x = 12 " ;

→ which is the answer.

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Hope this helps!

Best wishes in your academic pursuits

— and within the "Brainly" community!

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