Example Question - simplify exponential expressions
Here are examples of questions we've helped users solve.
Solving Exponential Operations
Para resolver la operación mostrada en la imagen, debemos aplicar la propiedad de exponentes que indica que cuando elevamos un producto a una potencia, podemos elevar cada factor a esa potencia. Usaremos la siguiente propiedad: \((ab)^n = a^n b^n\) La operación en la imagen es \((-7a^2b^3)^2\). Aplicando la regla de los exponentes, podemos resolver: \[ (-7a^2b^3)^2 = (-7)^2 (a^2)^2 (b^3)^2 \] Ahora, elevamos cada factor al cuadrado individualmente: \[ (-7)^2 = 49 \] \[ (a^2)^2 = a^{2\cdot2} = a^4 \] \[ (b^3)^2 = b^{3\cdot2} = b^6 \] Por lo tanto, al combinar estos resultados, obtenemos: \[ (-7a^2b^3)^2 = 49a^4b^6 \] Este es el resultado de la operación dada.
Simplifying Exponential Expressions
The expression in the image shows \(z^8\) multiplied by \(\frac{1}{z^7}\). To simplify this expression, you can use the property of exponents that states when dividing like bases, you subtract the exponents: \(z^8 \cdot \frac{1}{z^7} = \frac{z^8}{z^7} = z^{8-7} = z^1 = z\) So the simplified form of the expression is \(z\).
Simplifying Exponential Expressions
To simplify the expression \(\frac{2^{n+1}}{2^n * 2}\), you can use the properties of exponents. Here is how you can simplify it step by step: 1. The expression \(\frac{2^{n+1}}{2^n * 2}\) can be rewritten by separating the terms in the denominator, so you have \(\frac{2^{n+1}}{2^n \cdot 2^1}\). 2. Now you can apply the quotient rule for exponents, which states that when dividing like bases, you subtract the exponents: \(\frac{2^{n+1}}{2^n}\) becomes \(2^{(n+1)-n} = 2^1 = 2\). 3. So now you have \(2 \div 2^1\). 4. Applying the division rule for exponents again (or recognizing that any number divided by itself is 1), you have \(2^1 \div 2^1 = 2^{1-1} = 2^0 = 1\). The simplified form of the expression is \(1\).
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