Week 12 flashcard

Front

What is the exponential form of the product of two radical expressions, \(\sqrt[4]{x^2} \cdot \sqrt[4]{x^{1}}\)?

Back

The exponential form is \(x^{\frac{3}{4}}\).

Front

How do you simplify the expression \(a^{\frac{15}{3}}\) in radical form?

Back

The simplified expression is \(a^5\).

Front

What is the process to simplify the expression \(\left(\frac{25x^2y^3}{75x^{7y^0}}\right)^4\) and ensure positive exponents only?

Back

The simplified expression is \(\frac{y^{12}}{3^4x^{20}}\).

Front

How do you rewrite the expression \(x^{\frac{1}{5}}\) in radical form?

Back

The radical form is \(\sqrt[5]{x}\).

Front

What is the value of \(m^{6}\)?

Back

The value is simply \(m^{6}\).

Front

What is the general rule for multiplying radical expressions?

Back

When multiplying radical expressions, you can combine the radicands under a single radical if they have the same index.

Front

How do you convert a radical expression to exponential form?

Back

To convert a radical expression to exponential form, use the rule \(\sqrt[n]{x} = x^{\frac{1}{n}}\).

Front

What is the significance of positive exponents in algebraic expressions?

Back

Positive exponents indicate the number of times a base is multiplied by itself, while negative exponents represent the reciprocal.

Front

How do you simplify expressions with fractional exponents?

Back

To simplify expressions with fractional exponents, convert them to radical form or apply the laws of exponents.

Front

What is the relationship between radical and rational exponents?

Back

Radical exponents can be expressed as rational exponents, where \(\sqrt[n]{x} = x^{\frac{1}{n}}\).