Example Question - exponent
Here are examples of questions we've helped users solve.
Calculating the Value of y
<p>Given \( y^2 = 125^{\frac{2}{3}} \times 343^{\frac{2}{3}} \).</p> <p>We can simplify this as:</p> <p> \( y^2 = (125 \times 343)^{\frac{2}{3}} \).</p> <p>Now calculate \( 125 \) and \( 343 \):</p> <p> \( 125 = 5^3 \) and \( 343 = 7^3 \). </p> <p>Thus, \( 125 \times 343 = 5^3 \times 7^3 = (5 \times 7)^3 = 35^3 \).</p> <p>Substituting back, we have \( y^2 = (35^3)^{\frac{2}{3}} = 35^{2} \).</p> <p>So, \( y = \sqrt{35^{2}} = 35 \).</p> <p>Therefore, the value of \( y \) is:</p> <p> \( y = 35 \).</p>
Simplifying a Mathematical Expression
<p>Start with the expression:</p> <p>\(\frac{15^{16}}{15^{4} \times (15^{2})^{3}}\)</p> <p>First, simplify \((15^{2})^{3}\):</p> <p>\((15^{2})^{3} = 15^{6}\)</p> <p>Now substitute back into the expression:</p> <p>\(\frac{15^{16}}{15^{4} \times 15^{6}}\)</p> <p>Combine the terms in the denominator:</p> <p>So, the denominator becomes \(15^{4 + 6} = 15^{10}\)</p> <p>Now the expression is:</p> <p>\(\frac{15^{16}}{15^{10}}\)</p> <p>Using the quotient rule of exponents:</p> <p>Subtract the exponents: \(15^{16 - 10} = 15^{6}\)</p> <p>Thus, the simplified expression is:</p> <p>\(15^{6}\)</p>
Converting Between Scientific Notation and Floating-Point Notation
<p>The mathematical concept requested in the image involves understanding and converting between scientific notation and floating-point notation. Typically, any number in scientific notation is written as \( a \times 10^n \), where \( 1 \leq |a| < 10 \) and \( n \) is an integer.</p> <p>To convert from floating-point to scientific notation, we must adjust the decimal point to fit the criteria for \( a \), and then determine the appropriate exponent \( n \) that \( 10 \) must be raised to.</p> <p>Looking at the options provided:</p> <p>\( 20 \times 10^{-06} \) can be adjusted to \( 2.0 \times 10^{1} \times 10^{-06} = 2.0 \times 10^{-05} \)</p> <p>\( 0.02 \times 10^{-03} \) can be adjusted to \( 2.0 \times 10^{-02} \times 10^{-03} = 2.0 \times 10^{-05} \)</p> <p>\( 2 \times 10^{-05} \) is already in scientific notation.</p> <p>Without any additional context or numerical values in the image to match the options against, all three options provided are valid representations of numbers in scientific notation adjusted from the given floating-point notation starting points.</p>
Understanding Exponential Notation
<p>Definisi eksponensial adalah:</p> <p>a^n = \underbrace{a \times a \times a \times \ldots \times a}_{n \text{ faktor}}</p> <p>Di mana \( a \) adalah basis dan \( n \) adalah eksponennya, yang menunjukkan jumlah kali basis \( a \) dikalikan dengan dirinya sendiri.</p>
Determining the Name of Mathematical Expression
The image contains a mathematical question asking for another name for the expression \( B^{3/9} \). Simplifying \( B^{3/9} \) by dividing both the numerator and the denominator of the exponent by their greatest common divisor, which is 3, we get \( B^{(3÷3)/(9÷3)} = B^{1/3} \). Now let's look at the answer options: A) \( B^2 \) B) \( \sqrt[3]{B} \) C) \( B^9 \) D) \( \sqrt[9]{B} \) The correct answer is B, \( \sqrt[3]{B} \), because an exponent of \( 1/3 \) is equivalent to the cube root of the base, in this case, \( B \).
Solving Equations with an Exponent
The image contains a mathematical expression, which appears to represent an equation: \( y = 3(x + 5)^7 \) However, you haven't provided a specific question to solve with this equation. Are you looking for the derivative, integral, a particular value, or something else? Please provide more information so I can assist you appropriately.
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