Answer:
c=7
d=5
Step-by-step explanation:
Exponential Equations
We need to recall some properties of exponentials to solve the equations:
[tex]x^a*x^b=x`{a+b}[/tex]
[tex]\displaystyle (x^a)^b=x^{ab}[/tex]
Equation A
[tex]\sqrt{448x^c}=8x^3\sqrt{7x}[/tex]
Squaring:
[tex](\sqrt{448x^c})^2=(8x^3\sqrt{7x})^2[/tex]
Simplifying the radicals:
[tex]448x^c=64x^6(7x)[/tex]
[tex]448x^c=448x^7[/tex]
If follows that
c=7
Equation B
[tex]\sqrt[3]{576x^d}=4x\sqrt[3]{9x^2}[/tex]
Raising to the third power:
[tex](\sqrt[3]{576x^d})^3=(4x\sqrt[3]{9x^2})^3[/tex]
[tex]576x^d=4^3x^3(9x^2)[/tex]
Operating
[tex]576x^d=64x^3(9x^2)=576x^5[/tex]
Thus:
d=5
