# Solve for d (1/2)^2*4^(3d)=1

Solve for d (1/2)^2*4^(3d)=1
Simplify.
Rewrite as .
Raise to the power of .
Apply the power rule and multiply exponents, .
Multiply by .
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Multiply by .
Rewrite as .
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Multiply by .
Use the power rule to combine exponents.
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Simplify the denominator.
Apply the product rule to .
One to any power is one.
Raise to the power of .
Multiply the numerator by the reciprocal of the denominator.
Multiply .
Rewrite as .
Use the power rule to combine exponents.
Simplify the right side.
Simplify the denominator.
Apply the product rule to .
One to any power is one.
Raise to the power of .
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Create equivalent expressions in the equation that all have equal bases.
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
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