PLEASE help
Choose an equivalent expression for three fourths raised to the fourth power times three fourths raised to the third power all raised to the second power.
nine sixteenths raised to the twenty fourth power
nine sixteenths raised to the fourteenth power
three fourths raised to the twenty fourth power
three fourths raised to the fourteenth power

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semsee45 semsee45 · Answer 1 · 2022-08-25T11:46:56+02:00

Answer:

[tex]\left(\dfrac{3}{4}\right)^{14}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(\left(\dfrac{3}{4}\right)^4 \times \left(\dfrac{3}{4}\right)^3\right)^2[/tex]

[tex]\textsf{Apply the product rule of exponents} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies \left(\left(\dfrac{3}{4}\right)^{4+3}\right)^2[/tex]

[tex]\implies \left(\left(\dfrac{3}{4}\right)^{7}\right)^2[/tex]

[tex]\textsf{Apply the power of a power rule of exponents} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \left(\dfrac{3}{4}\right)^{7\times 2}[/tex]

[tex]\implies \left(\dfrac{3}{4}\right)^{14}[/tex]

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